Statistical Intervals Based on a Single Sample

Chapter
Part of the Springer Texts in Statistics book series (STS)

Abstract

A point estimate, because it is a single number, by itself provides no information about the precision and reliability of estimation. Consider, for example, using the statistic \( \overline{X} \) to calculate a point estimate for the true average breaking strength (g) of paper towels of a certain brand, and suppose that \( \overline{{x}} = {9322}.{7} \). Because of sampling variability, it is virtually never the case that \( \overline{{x}} = \mu \).

Bibliography

  1. DeGroot, Morris, and Mark Schervish, Probability and Statistics (3rd ed.), Addison-Wesley, Reading, MA, 2002. A very good exposition of the general principles of statistical inference.Google Scholar
  2. Efron, Bradley, and Robert Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993. The bible of the bootstrap.CrossRefGoogle Scholar
  3. Hahn, Gerald, and William Meeker, Statistical Intervals, Wiley, New York, 1991. Everything you ever wanted to know about statistical intervals (confidence, prediction, tolerance, and others).CrossRefGoogle Scholar
  4. Larsen, Richard, and Morris Marx, Introduction to Mathematical Statistics (4th ed.), Prentice Hall, Englewood Cliffs, NJ, 2005. Similar to DeGroot’s presentation, but slightly less mathematical.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Statistics DepartmentCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsIllinois State UniversityNormalUSA

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